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Research Article | Open Access

Existence of solutions of Dirichlet problems for one dimensional fractional equations

Armin Hadjian1( ), Juan J. Nieto2
Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, P.O. Box 1339, Bojnord 94531, Iran
CITMAga, Institute of Mathematics, University of Santiago de Compostela, Santiago de Compostela 15782, Spain
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Abstract

We establish the existence of infinitely many solutions for some nonlinear fractional differential equations under suitable oscillating behaviour of the nonlinear term. These problems have a variational structure and we prove our main results by using a critical point theorem due to Ricceri.

Keywords

fractional differential equationsCaputo fractional derivativesinfinitely many solutionsvariational methods
CLC number: 34A08, 35A15, 26A33

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AIMS Mathematics
Volume 7 Issue 4,
April 2022
Pages 6034-6049
DOI: 10.3934/math.2022336

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Cite this article:
Hadjian A, Nieto JJ. Existence of solutions of Dirichlet problems for one dimensional fractional equations. AIMS Mathematics, 2022, 7(4): 6034-6049. https://doi.org/10.3934/math.2022336

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Received: 07 September 2021
Revised: 13 December 2021
Accepted: 29 December 2021
Published: 15 April 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)